Cox Proportional Hazards Model

Halley Deleeuw and Jasmine Sawh

2023-11-30

Introduction to Cox Proportional Hazards Model

  • Developed by Sir David R. Cox in 1972
  • Statistical method for survival analysis and epidemiological research
  • Analyzes time-to-event data
  • Estimates hazard function
  • Explores relationships with independent variables
  • Applications include healthcare, engineering, social sciences

Methods

  • Semiparametric survival analysis method
  • Right-censored data \[ λ(t) = λ0(t) * exp(β₁X₁ + β₂X₂ + ... + βₖ) \]

Assumptions/Limitations

  • Proportional Hazard Assumption
  • Linearity of Continuous Variables
  • Independence of Censoring
  • Sensitivity to Outliers

Data Description

  • National Cancer Institute Surveillance, Epidemiology, and End Results Program (SEER)
  • Comprehensive cancer surveillance system in the US
  • Covers a wide range of demographic information
  • Provides insights into cancer trends, outcomes, and risk factors at a national level

Data Table

Data Visualization

Objective and Purpose

  • Explore factors impacting patient survival
  • Analyze key variables such as cancer type, race, gender, age
  • Understanding their significance in predicting survival
  • Assess hazard ratios for each variable
  • Center analysis on relationships and impact on survival outcomes

Statistical Modeling for Data

Stratified Analysis

Analysis on Deceased Patients

Adding an Interaction term to Filtered Analysis on Deceased Patients

Data Analysis with Reference Categories

Model with Time-Dependent Covariates

Conclusion

  • Identified key predictors impacting cancer survival
  • Explored survival dynamics
  • Proportional Hazards assumption violated
  • Stratification, Interaction Term, Time-Dependent covariates

References

Anna Vadeby, Goran Kecklund, Asa Forsman. 2010. “Sleepiness and Prediction of Driver Impairment in Simulator Studies Using a Cox Proportional Hazard Approach.” Research Article.

Faruk, Alfensi. 2018. “The Comparison of Proportional Hazards and Acceleratedfailure Time Models in Analyzing the First Birth Interval Survival Data.” Research Article.

Ilari Kuitunen, Mikko M. Uimonen, Ville T. Ponkilainene. 2021. “Testing the Proportional Hazards Assumption in Cox Regression and Dealing with Possible Non-Proportionality in Total Joint Arthroplasty Research: Methodological Perspectives and Review.” Research Article.

J Martin Bland, Douglas G Altman. 2004. “The Logrank Test.” Research Article. Jaime Gonzalez-Dominguez, Justo Garcia-Sanz-Calcedo, Gonzalo Sanchez-Barroso. 2022. “Cox Proportional Hazards Model Used for Predictive Analysis of the Energy Consumption of Healthcare Buildings.” Research Article.

Jianqing Fan, Runze Li. 2002. “Variable Selection for Cox’s Proportional Hazards Model and Frailty Model.” Research Article.

John Fox, Sanford Weisberg. 2023. “Cox Proportional-Hazards Regression for Survival Data in r.” Research Article.

Lucas Equeter, Edouard Riviere-Lorphevre, Francois Ducobu. 2020. “An Analytic Approach to the Cox Proportional Hazards Model for Estimating the Lifespan of Cutting Tools.” Research Article.

Ofir Ben-Assuli, Tsipi Heart, Roni Ramon-Gonen. 2023. “Utilizing Shared Frailty with the Cox Proportional Hazards Regression: Post Discharge Survival Analysis of CHF Patients.” Research Article.

Salil Vasudeo Deo, Varun Sundaram, Vishali Deo. 2021. “Survival Analysis—Part 2: Cox Proportional Hazards Model.” Research Article.

Ville T. Ponkilainene, Antti Eskelinen, Mikko M. Uimonen. 2021. “Testing the Proportional Hazards Assumption in Cox Regression and Dealing with Possible Non-Proportionality in Total Joint Arthroplasty Research.” Research Article.

W. W. M. Abeysekera, M. R. Sooriyarachchi. 2009. “Use of Schoenfeld’s Global Test to Test the Proportional Hazardsassumption in the Cox Proportional Hazards Model: An Application to a Clinical Study.” Research Article.